Difficult PSLE 2009 Mathematics Question

Jim bought some chocolates and gave half of it to Ken. Ken bought some sweets and gave half of it to Jim. Jim ate 12 sweets and Ken ate 18 chocolates. The ratio of Jim’s sweets to chocolates became 1:7 and the ratio of Ken’s sweets to chocolates became 1:4. How many sweets did Ken buy?

Assume,
Jim bought x chocolates.
Ken bough y sweets.

Chocolates
Jim : Ken
1/2 x : 1/2 x (after Jim gave half of x to Ken)
1/2 x : 1/2 x - 18 (after Ken ate 18 chocolates)

Sweets
Jim : Ken
1/2 y : 1/2 y (after Ken gave half of y to Jim)
1/2 y - 12 : 1/2 y (after Jim ate 12 sweets)

Therefore,
Jim's sweets : Jim's Chocolates
1 : 7 (given)
1/2 y - 12 : 1/2 x
=> 7(1/2 y - 12) = 1/2 x
7y - 168 = x -------------------(1)

Ken's sweets: Ken's Chocolates
1: 4 (given)
1/2 y : 1/2 x - 18
=> 4(1/2 y) = 1/2 x - 18
x = 4y + 36 ---------------------(2)

Solving (1) = (2),
We get y = 68 (Answer)





i was never expected to understand this at age 12.
no wonder parents are "up in arms" again.

oh yes, the above answer is mine. verified correct by the media :)